Theorem 2 Let \(\mu \)  be a measure on a locally compact space, \(X\)  with \(L^2 (X,d\mu )\)  separable.
Let \(L_0\)  be a selfadjoint operator on \(L^2(X,d\mu )\)  so that its semigroup is ultracontractive
([1]}): For some \(s>0\) , \(e^{-sL_0}\)  maps \(L^2\)  to \(L^\infty (X,d\mu )\) . Suppose
\(V\)  is a nonnegative multiplication operator so that
\( \mu (\lbrace x\mid 0\le V(x) <M\rbrace ) <\infty \) 
